TAILIEUCHUNG - Andoyer equations for noncollinear planar central configurations

In this article we obtain the Andoyer equations for noncollinear planar central configurations taking into account the center of mass of the system. We apply these equations to study two configurations. In the first one we prove that it is not possible to put a square central configuration and an equilateral triangle central configuration as a cocircular central configuration. | Turk J Math (2017) 41: 515 – 523 ¨ ITAK ˙ c TUB ⃝ Turkish Journal of Mathematics doi: Research Article Andoyer equations for noncollinear planar central configurations Antonio Carlos FERNANDES, Luis Fernando MELLO∗ Institute of Mathematics and Computa¸ca ˜o, Federal University of Itajub´ a, Itajub´ a, MG, Brazil Received: • Accepted/Published Online: • Final Version: Abstract: In this article we obtain the Andoyer equations for noncollinear planar central configurations taking into account the center of mass of the system. We apply these equations to study two configurations. In the first one we prove that it is not possible to put a square central configuration and an equilateral triangle central configuration as a cocircular central configuration. In the second one we give the central configurations for the noncollinear planar 4 –body problem with one pair of equal positive masses and two null masses. Key words: Central configuration, n –body problem, planar central configuration, celestial mechanics 1. Introduction and statement of the main results The classical Newtonian n –body problem consists of the study of a system formed by n punctual bodies with positives masses m1 , . . . , mn interacting by Newton’s gravitational law [11]. That is, if the position vectors are given by r1 , . . . , rn in Rd , d = 2, 3, the equations of motion are r¨i = Fi = − n ∑ mj j=1 j̸=i 3 rij (ri − rj ), (1) for i = 1, . . . , n, where rij =

• Toán học
• Central configuration
• N–body problem
• Planar central configuration
• Celestial mechanics
• Noncollinear planar
• N body problem
• Inverse problem of central configuration
• Collinear general 4
• 5 body problems